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Hannes Leitgeb (2002). What is a Self-Referential Sentence? Critical Remarks on the Alleged Mbox(Non-)Circularity of Yablo's Paradox.

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  1.  68
    Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
    We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo (...)
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  2.  30
    Yablo's Paradox in Second-Order Languages: Consistency and Unsatisfiability.Lavinia María Picollo - 2013 - Studia Logica 101 (3):601-617.
    Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order (...)
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  3.  51
    The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth.P. Schlenker - 2007 - Journal of Philosophical Logic 36 (3):251-307.
    Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo's (...)
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  4.  46
    How to Eliminate Self-Reference: A Précis.Philippe Schlenker - 2007 - Synthese 158 (1):127-138.
    We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h 0(F), h 1(F), ..., stated in a quantificational language L *. Under certain conditions, we show that none of the translations is self-referential, but that any one (...)
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  5. Paradox by (Non-Wellfounded) Definition.Hannes Leitgeb - 2005 - Analysis 65 (4):275–278.